In addition to the maximum clique problem, there is another large class of optimization
problem for which the OGP approach provides a tight
classification of solvable vs not yet solvable in polynomial time problems.
It is the problem of finding ground states of p-spin models – the
very class of optimization problems which led to studying the overlap distribution
and overlap gap type properties to begin with. The problem is described
as follows: suppose one is given a \(p\) -order tensor \(J\)  of side length \(N\) .
Namely, \(J\)  is described as a collection of real values \(J_{i_1,\ldots ,i_p}\) 
where \(i_1,\ldots ,i_p\)  range between 1 and \(N\) . Given the solution space \(\Sigma _N\) ,
the goal is finding a solution \(\sigma \in \Sigma _N\) 
(called ground state) which
minimizes the inner product
\(\langle J,\sigma \rangle =\sum _{i_1,\ldots ,i_p}J_{i_1,\ldots ,i_p}\sigma _{i_1}\cdots \sigma _{i_p}\) .
The randomness
in the model is derived from the randomness of the entries of \(J\) . A common assumption,
capturing most of the structural and algorithmic complexity
of the model, is that the entries \(J_{i_1,\ldots ,i_p}\)  are independent standard normal entries.
Two important
special cases of the solution space \(\Sigma _N\)  include the case when \(\Sigma _N\) 
is a binary cube \(\lbrace -1,1\rbrace ^N\) , and when it is a sphere of a fixed radius (say 1) in the
\(N\) -dimensional real space, the latter case being referred to as spherical spin glass model.
The special case \(p=2\)  and \(\Sigma _N=\lbrace -1,1\rbrace ^N\) 
is the celebrated Sherrington-Kirkpatrick model [1]} – the centerpiece of the spin glass theory.
The problem of computing the value of this
optimization problem above was at the core of the spin glass theory in the past four decades,
which led to the replica symmetry breaking technique
first introduced in the physics literature by Parisi [2]},
and then followed by a series of mathematically rigorous
developments, including those by Talagrad [3]} and Panchenko [4]}.
